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Article overview
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Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules | Martin Greiter
; F.D.M. Haldane
; Ronny Thomale
; | Date: |
23 May 2019 | Abstract: | We use a family of critical spin chain models discovered recently by one of
us [M. Greiter, Mapping of Parent Hamiltonians, Springer, Berlin/Heidelberg
2011] to propose and elaborate that non-Abelian, SU(2) level $k=2S$ anyon
statistics manifests itself in one dimension through topological selection
rules for fractional shifts in the spacings of linear momenta, which yield an
internal Hilbert space of, in the thermodynamic limit degenerate states. These
shifts constitute the equivalent to the fractional shifts in the relative
angular momenta of anyons in two dimensions. We derive the rules first for
Ising anyons, and then generalize them to SU(2) level $k$ anyons. We establish
a one-to-one correspondence between the topological choices for the momentum
spacings and the fusion rules of spin half spinons in the SU(2) level $k$
Wess--Zumino--Witten model, where the internal Hilbert space is spanned by the
manifold of allowed fusion trees in the Bratelli diagrams. Finally, we show
that the choices in the fusion trees may be interpreted as the choices between
different domain walls between the $2S+1$ possible, degenerate dimer
configurations of the spin $S$ chains at the multicritical point. | Source: | arXiv, 1905.9728 | Services: | Forum | Review | PDF | Favorites |
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